I currently have an 8' x10' patio cover constructed of side by side 2x6's that are painted. I want to cover the 2x6's with plywood covered with tar paper and then covered with a thin layer of cement. I would then seal the cement with a colored sealer containing sand to give the surface a sandpaper texture. This cover is exposed to the sun and rain in the Southern California area. Is this a good approach for sealing a patio cover?

When you say 'patio cover' do you mean a roof for the patio? If you reconstruct it the way you want, it will be far too heavy. Everything you suggest will break down eventually in the California sun and rain and I wouldn't want to be sitting under it when that happened. I don't know about your building permits in California and your building codes, plus liability insurance, but this is not feasible.

Tick

You can't put a thin layer of cement (concrete) on tar paper, plywood, or anything except concrete. It will crumble in less than a month.
Is this a flat roof? Rubber roofing is the only good way.
If slightly sloped, any roofing material.
Since 8 x 10 is small, a retractable awning might be a good option. You might miss some sunny days through the roof?

What is the slope? Are there roof joists? If at least a 3/12 and joists, why not an architectural 3 tab shingle?